First, reference is made to sequences that are used in OFDM, OFDMA, and 3GPP LTE systems to which the above methods are applied.
Recently, the demand for high-speed data transmission has rapidly increased. The OFDM scheme is advantageous for high-speed transmission and thus has been adopted as a transmission scheme for a variety of high-speed communication systems. The following is a description of Orthogonal Frequency Division Multiplexing (OFDM). The basic principle of the OFDM is to divide a high-rate data stream into a large number of low-rate data streams and to simultaneously transmit the low-rate data streams through a number of carriers. Each of the carriers is called a subcarrier. Since the subcarriers of the OFDM are orthogonal to each other, it is possible for the receiving side to detect the frequency components of the subcarriers even if they overlap each other. The high-rate data stream is converted into multiple low-rate data streams through a serial-to-parallel converter. The parallel low-rate data streams produced through the conversion are multiplied by respective subcarriers and are then combined to be transmitted to the receiving side. The OFDMA is a multiple access method which allocates subcarriers in a total band in the OFDM system to multiple users according to transfer rates requested by the users.
The OFDM scheme has a problem in that the Peak-to-Average-Power Ratio (PAPR) or Cubic Metric (CM) of transmission signals is very high. Since the OFDM scheme transmits an OFDM signal in the frequency domain using multiple subcarriers through IFFT, the magnitude of the amplitude of the OFDM signal can be represented by the sum of the magnitudes of the multiple subcarriers. However, if the multiple subcarriers are in phase with each other, a signal having a high peak similar to an impulse occurs in the OFDM signal, thereby causing the OFDM signal to have a very high PAPR or CM. Such transmission signals according to the OFDM reduce the efficiency of a high-output linear amplifier and operate in a nonlinear region of the high-output linear amplifier, thereby causing signal distortion.
The following is a description of channels and sequences for use in the channels in a newly-proposed 3rd Generation Partnership Project (3GPP) Long Term Evolution (LTE) system.
Generally, in order to perform communication with a base station, a terminal (or user equipment) first carries out synchronization with the base station over a synchronization channel (SCH) and conducts a cell search. The SCH may have a hierarchy such that it is divided into a Primary Synchronization channel (P-SCH) and a Secondary Synchronization channel (S-SCH).
The cell search is a series of processes that a terminal performs to acquire the ID of a cell to which the terminal belongs. The cell search is generally classified into an initial cell search, which a terminal performs when it is powered on, and a neighbor cell search through which a terminal in a connected or idle mode searches for a neighbor base station.
It is preferable that the P-SCH used in a communication system such as OFDM or SC-FDMA, which uses multiple orthogonal subcarriers, satisfy the following requirements.
First, auto-correlation properties in the time domain for SCH sequences should be good to allow the receiving side to achieve high detection performance.
Second, the complexity due to synchronization detection should be low.
Third, the Peak-to-Average Power Ratio (PAPR) or CM should be low.
Fourth, if an SCH can be used for channel estimation, it is desirable that its frequency response have a constant value. That is, it is known that a flat response in the frequency domain exhibits the best channel estimation performance.
A type of sequence, which is under discussion for use in channels that are used in the LTE including the SCH described above, is a Zadoff-Chu sequence which is a Constant Amplitude Constant Auto-Correlation (CAZAC)-type sequence.
Two types of CAZAC sequences, which are mainly used, are Generalized Chirp-Like (GCL) CAZAC and Zadoff-Chu CAZAC sequences. The Zadoff-Chu CAZAC sequence is given as follows.
                                          a            M                    ⁡                      (            n            )                          =                                  ⁢                                  ⁢                  {                                                                                          exp                    ⁡                                          (                                                                        -                          j                                                ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                                              Mn                            2                                                    /                          L                                                                    )                                                        ,                                                                              when                  ⁢                                                                          ⁢                  L                  ⁢                                                                          ⁢                  is                  ⁢                                                                          ⁢                  even                                                                                                                          exp                    ⁡                                          (                                                                        -                          j                                                ⁢                                                                                                  ⁢                        π                        ⁢                                                                                                  ⁢                                                                              Mn                            ⁡                                                          (                                                              n                                +                                1                                                            )                                                                                /                          L                                                                    )                                                        ,                                                                                                  when                    ⁢                                                                                  ⁢                    L                    ⁢                                                                                  ⁢                    is                    ⁢                                                                                  ⁢                    odd                                    ,                                                                                        MATHEMATICAL        ⁢                                  ⁢        EXPRESSION        ⁢                                  ⁢        1            
where “n” denotes a sequence index, “L” denotes the length of the CAZAC sequence, and “M” denotes a sequence ID. Here, “M” can be represented by a set of natural numbers which are relatively prime to “L”.
When the Zadoff-Chu (ZC) CAZAC sequence given as Mathematical Expression 1 is represented by c(k;N,M), it has the following three properties.
                                                                    c              ⁡                              (                                  k                  ;                  N                  ;                  M                                )                                                          =          1                ⁢                                  ⁢                  (                                    for              ⁢                                                          ⁢              all              ⁢                                                          ⁢              k                        ,            N            ,            M                    )                                    MATHEMATICAL        ⁢                                  ⁢        EXPRESSION        ⁢                                  ⁢        2                                                      R            MN                    ⁡                      (            d            )                          =                  {                                                                      1                  ,                                                                              (                                                            for                      ⁢                                                                                          ⁢                      d                                        =                    0                                    )                                                                                                      0                  ,                                                                              (                                                            for                      ⁢                                                                                          ⁢                      d                                        ≠                    0                                    )                                                                                        MATHEMATICAL        ⁢                                  ⁢        EXPRESSION        ⁢                                  ⁢        3                                                      R                                          M                1                            ,                                                M                  2                                ;                N                                              ⁡                      (            d            )                          =                  p          ⁢                                          (                                    for              ⁢                                                          ⁢              all              ⁢                                                          ⁢                              M                1                                      ,                                          M                2                            ⁢                                                          ⁢              and              ⁢                                                          ⁢              N                                )                                    MATHEMATICAL        ⁢                                  ⁢        EXPRESSION        ⁢                                  ⁢        4            
Mathematical Expression 2 indicates that the magnitude of the CAZAC sequence is always 1 and Mathematical Expression 3 indicates that the auto-correlation function of the CAZAC sequence is represented by a delta function. Here, the auto-correlation is based on circular correlation. Mathematical Expression 4 indicates that the cross-correlation always has a constant value if “N” is a prime number.
In the case of CAZAC sequences, a total of L−1 sequences can be generated if the required length “L” of each sequence is a prime length. However, the number of sequences that can be generated is significantly reduced if the sequence length “L” is not a prime length. The following are methods which can be suggested to solve the problem in the case where the sequence length “L” required for a communication system is not a prime length due to the resource block length or the like.
One of the methods is a truncated sequence generation method.
FIG. 1 illustrates a method of generating sequences according to the truncated sequence generation method.
In this method, when a length “L” required in the system is not a prime length, a prime “X” greater than the length “L” is used as the length “L” in Mathematical Expression 1 to generate sequences. Thereafter, sequences with a length greater than “L” among the generated sequences are truncated to the length “L”.
The truncated sequence generation method can increase the number of sequences. However, since the truncated sequence generation method truncates generated sequences, the method degrades both the auto-correlation property, which requires that the auto-correlation have a value of “1” when the delay is zero and have a value of “0” when the delay is not zero as represented in Mathematical Expression 3, and the cross-correlation property which requires that the cross-correlation always have a constant value as represented in Mathematical Expression 4. In addition, if sequences with bad correlation properties are removed, it cannot be guaranteed that the number of sequences is L−1. Truncating the generated CAZAC sequences may also degrade the low-PAPR properties of CAZAC sequences.
In One technique that has been suggested to overcome these problems, a maximum prime length “X” less than the length “L” required in the communication system is selected to generate a CAZAC sequence and padding is inserted into a portion having a length of “L−X”.
FIG. 2 illustrates a method of generating sequences according to the padded sequence generation method.
According to the padded sequence generation method, if a length “L” required in the system is not a prime length, a prime “X”, which is the greatest among primes less than the length “L”, is used as the length “L” in Mathematical Expression 1 to generate a sequence. Thereafter, a zero padding having a length C2 corresponding to “L−X” is added to the generated sequence C1.
In this padded sequence generation method, the portion for correlation calculation of the sequence is set to the C1 portion of FIG. 2 to identify the sequence, thereby preventing the degradation of the auto-correlation and cross-correlation properties that would occur due to the truncation of generated sequences as shown in FIG. 1. However, the padded sequence generation method may also suffer from the degradation of the correlation and PAPR properties due to the zero padding C2 in consideration of the entire length of the sequence generated according to the method.
One method similar to that described with reference to FIG. 2 is a cyclic extension method. In the cyclic extension method, if the length “L” required in the system is not a prime length, a prime “X”, which is the greatest among primes less than the length “L”, is used as the length “L” in Mathematical Expression 1 to generate a sequence. Thereafter, a portion having a length C2 corresponding to “L−X” is copied from part of a previously generated sequence and is then added to the generated sequence C1 to generate a sequence having a length “L”.
This method can reduce the degradation of the correlation and PAPR properties, compared to the zero-padded sequence generation method.
The following is a description of the case of generation of a set of two or more sequences for use in a specific channel.
Important considerations, when designing sequences in a sequence-based transport channel taking into consideration the above facts, include the Peak-to-Average Power Ratio (PAPR) or Cubic Metric (CM) properties, the (periodic and aperiodic) auto/cross-correlation properties, etc.
However, in the case where a set of two or more sequences for use in a specific channel is generated using sequences generated based on the same length or using the same type of sequences, it is difficult to satisfy all the requirements that the PAPR or CM properties, the correlation properties, etc., be better than a certain level.